The purpose of the research proposed here is to investigate the applicability of two recently developed non-linear dynamical models, fractals and self-organization, to biomembrane structure/fluidity dynamics, and to thylakoid membrane stacking and domain formation in particular. Molecular mobility is an important determinant of metabolic rates in biomembranes, particularly for enzymes and substrates that are spatially restricted, as in portions of the photosynthetic and respiratory electron transport chains. Biomembranes are heterogeneous, disordered media that may possess fractal geometry. The simplest fractal theoretical model, which is in the process of being applied to biomembranes by a number of workers, is the percolation model. Recent theoretical investigations have suggested that transport properties, such as diffusion and conduction, are anomalous on percolation lattices. The diffusion constant has been shown to depend on the length scale of measurement and the rate coefficient of bimolecular reactions, a constant in homogeneous reaction spaces, has been shown to be time dependent. Chloroplast thylakoid membrane stacking provides a superb apparatus for the study of structure/function interactions in biomembranes, especially as they relate to molecular mobility within the membrane domain. A number of workers have recently proposed a percolation model of chloroplast thylakoid membrane microstructure that accounts for a diversity of heretofore puzzling experimental observations, in which mobility is restricted by the formation of extended microdomains of thylakoid membrane proteins within stacked thylakoids. We propose to explore the hypotheses that (l) biomembranes, including thylakoids, may be regarded as spaces that have the geometry of random fractals; and (2) domain formation within the chloroplast thylakoid membrane reflects a non-linear dynamical process involving self- organization of integral thylakoid membrane proteins. We propose theoretical studies in which we will determine how fluorescence quenching data may be used to quantify molecular mobility in these spaces and investigate the application of the percolation model to fluid percolation lattices, develop and solve a kinetic model for thylakoid membrane domain formation and stacking based on nonlinear differential equations, and investigate the effects of membrane geometry alone on protein aggregation patterns and of multiple protein populations. We also propose experimental studies in which we will estimate diffusion coefficients using the fluorescence quenching technique, both in the vapor phase and in progressively complex condensed phases, from simple organic solutions to disordered heterogeneous systems such as liposomes and proteoliposomes and finally to structured systems such as lipid-enriched thylakoid grana, extend the measurement time/distance scale beyond those accessible by fluorescence quenching measurements by studying phosphorescence and nmr kinetics; and conduct a feasibility study of spectroscopic, biochemical and ultrastructural methods of investigation.